Nevertheless living in the Netherlands I visit Bruges a few times a month as it is just a 40min. drive from my place and am I also quite familiar with the nearby places.
You can ofcourse contact the campsite if they know a nearby grocery that is open on Sundays.
Shops in Belgium are free about opening/closing times. In general however the larger supermarkets like Delhaize, Carrefour and Colruyt will be closed, but some branches, mostly smaller ones like Carrefour Express can be open in the morning, till early afternoon or even the whole day. It differs from place to place, I see that a Carrefour near the railway station in Ypres will be open on sunday till 6PM.
If you can be more precise about the route to drive from the airport to Ypres and also the time of arrival I can help looking for a grocery along the road as close as possible to the freeways that will be open. The most obvious route to follow from Brussels Airport is direction E40 to Gent, near Gent direction E17 to Kortrijk, there E403 and E19 to Ieper (Ypres), so will this be the route you are planning?
I don’t see so many campsites just east of Bruges on google maps, just guessing will it be Camping Memling in Sint-Kruis? If so the Brico shop and the A.S. Adventure shop are at walking distance as well as a bus stop for going to the historic centre. Carrefour Express (that is not the large one next to the Brico shop) in Sint-Kruis is open till 8PM but located further away along the Moerkerkse Steenweg.